On the Reidemeister moves of a classical knot
On the Reidemeister moves of a classical knot
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论古典结的雷德迈斯特动作
DOI：
10.1090/s0002-9939-1983-0719004-4
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发表时间：
1983
影响因子：
0.8
通讯作者：
B. Trace
中科院分区：
文献类型：
--
作者：
B. Trace
我们表明，在一定的合理标准下，Reidemeister移动之一，可以elminate。经典纽结理论中的一个众所周知的事实是，下面的三个移动，称为Reidemeister移动，产生了一个纽结的所有可能的投影。更精确地说，给定R3中的两个定向结点K1和K2，其中K1相对于自然投影7：R3 R2处于一般位置，具有存在将K1携带到K2并保持结点的定向的合痕的性质，则存在将K1携带到K2并保持结点的定向的Reidemeister移动序列。请注意，最后两个Reidemeister移动保留了结投影的两个属性。
We show that under certain reasonable criteria one of the Reidemeister moves can be elminated. It is a well-known fact in classical knot theory that the following three moves, known as the Reidemeister moves, generate all the possible projections of a knot. To be more precise, given two oriented knots, K, and K2, in R3, where K, is in general position with respect to the natural projection 7: R3 R2, having the property that there is an isotopy carrying K, to K2 and preserving the orientations of the knots, then there is a sequence of the Reidemeister moves taking K, to K2 and preserving the orientations of the knots. Note that the last two Reidemeister moves preserve two properties of the knots projection.